Before the 1957 season, Leo Burke was signed by the Baltimore Orioles as an amateur free agent. They placed him with the class A Knoxville Smokies where he appeared in 97 games, hitting .192. This prompted a hitting lesson trip to the AA San Antonio Missions where he got into 22 games and hit .183.

Evidently the tutoring helped as 1958 saw Leo hit .307 with 17 homers for Knoxville and earned him a late-season look from Baltimore, where he appeared in seven games. He had 11 at-bats with 5 base hits, including one home run and a .455 hitting average.

Burke was with the AAA Miami Marlins in 1959 where he dropped back to .219 but had 21 four-baggers and got another late-season trip to Baltimore, getting into five games with a .200 batting average. It was back to Miami for the entire season in 1960, where he had 15 homers and hit .255. On December 14th the Washington Senators plucked him from the Orioles in the expansion draft and in turn sold Leo to the Los Angeles Angels, their brothers in expansion.

Leo made six appearances with the Angels in 1961, did not make an impression and was sent to the Dallas-Fort Worth Rangers where he hit .252 in 42 games and wound up for the balance of the year with the Salt Lake City Bees. With the Bees he was in 90 contests, hit 16 homers and had a .280 batting average.

Burke spent his first and only full season in the major leagues with the Cubs in 1964, hitting .262. Leo spent 12 games with the Cubs in 1965; he went 2 for 10 and they sent him to the Salt Lake City Bees, where he appeared in 60 games and hit .214. He then decided he would close his career in professional baseball.

Burke spent nine active seasons in pro baseball from 1957 through 1965. He was in and out of the majors seven different seasons but he appeared in 165 games, had 301 at-bats with 72 base hits, including 9 home runs and a .239 career batting average. His minor league stats show a bit more action, appearing in 844 games, with 2,875 at bats and 732 base hits, including 127 home runs and a .254 career batting average.

He was a graduate in business administration from Virginia Tech, where he played baseball, basketball and football. As of December, 2008, he was retired in his hometown of Hagerstown, MD.